Lattice distortion and octupole ordering model in Ce_xLa _1-xB₆

Possible order parameters of the phase IV in Ce_xLa _1-xB₆ are discussed with special attention to the lattice distortion recently observed. A Γ_5u-type octupole order with a finite wave number is proposed as the origin of the distortion along the [111] direction. The Γ₈ crystalline electric field (CEF) level splits into three levels by a mean field with the Γ_5u symmetry. The ground and highest singlets have the same quadrupole moment, while the intermediate doublet has an opposite sign. It is shown that any collinear order of the Γ_5u-type octupole moment accompanies the Γ_5g-type ferro-quadrupole order, and the coupling of the quadrupole moment with the lattice induces the distortion. The cusp in the magnetization at the phase transition is reproduced, but the internal magnetic field due to the octupole moment is smaller than the observed one by an order of magnitude.